Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15689559 | C2 | semidirect |
| 2. C2×#15689390 | C2 | semidirect |
| 3. #20253060 | C2 | semidirect |
| 4. C2×#15688931 | C2 | semidirect |
| 5. C2×#15688906 | C2 | semidirect |
| 6. #20241496 | C2 | semidirect |
| 7. C2×C47×#357 | C2 | semidirect |
| 60. #13093964 | D4 | semidirect |
| 63. #13093960 | D4 | semidirect |
| 73. C2×D8×C47 | D4 | semidirect |
| 215. C2×#357 | D47 | semidirect |
| 249. C47 | #13307 | semidirect |
| 269. C2×D8 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689559 | 2 |
| C2×#15689390 | 2 |
| #20253060 | 2 |
| C2×#15688931 | 2 |
| C2×#15688906 | 2 |
| #20241496 | 2 |
| C2×C47×#357 | 2 |
| #13307 | 47 |